Chapter 10. Newton's law of universal gravitation (10-2)

Question

+/TlAhYplKaVk2nfmPUn2/GImZ8wTStVPDq1gZ613HSx0NwafQvIkVTslQpxcskDwx9lvc8C7VaNJY/tET3rUcX5/fCV8rChefp38l6XlKY=
{"title":"Any two objects exert equally strong gravitational forces on each \perpher.","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"1,23,28,63\"},{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"102,19,133,60\"}]"} {"title":"Gravitational constant (same for any two objects)","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"201,1,230,32\"}]"} {"title":"Masses of the two objects","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"poly\",\"coords\":\"113,132\"},{\"shape\":\"rect\",\"coords\":\"263,4,289,30\"},{\"shape\":\"rect\",\"coords\":\"231,3,253,33\"}]"} {"title":"Center-to-center distance between the two objects","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"235,52,255,73\"}]"} {"title":"The gravitational forces are attractive: vector F sub 1 on 2 pulls object 2 toward object 1 and vector F sub 2 on 1 pulls object 1 toward object 2.","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"32,40,56,59\"},{\"shape\":\"rect\",\"coords\":\"134,42,156,61\"}]"}

Question

IXtGBQA1joLagfMl7P/XK+iTjqsOtvP3vNI4DACZEChoy5C2AWObgo3PTFXgWQS9I3KHm67ErtjgIU00RvzBwqWEE1g=
{"title":"Any two objects exert equally strong gravitational forces on each \perpher.","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"1,23,28,63\"},{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"102,19,133,60\"}]"} {"title":"Gravitational constant (same for any two objects)","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"201,1,230,32\"}]"} {"title":"Masses of the two objects","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"poly\",\"coords\":\"113,132\"},{\"shape\":\"rect\",\"coords\":\"263,4,289,30\"},{\"shape\":\"rect\",\"coords\":\"231,3,253,33\"}]"} {"title":"Center-to-center distance between the two objects","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"235,52,255,73\"}]"} {"title":"The gravitational forces are attractive: vector F sub 1 on 2 pulls object 2 toward object 1 and vector F sub 2 on 1 pulls object 1 toward object 2.","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"32,40,56,59\"},{\"shape\":\"rect\",\"coords\":\"134,42,156,61\"}]"}

Question

tfDBnh/BepSwtrb1e/2zgz5IuSepnnA6sPKyVRXnm+k=
{"title":"Any two objects exert equally strong gravitational forces on each \perpher.","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"1,23,28,63\"},{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"102,19,133,60\"}]"} {"title":"Gravitational constant (same for any two objects)","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"201,1,230,32\"}]"} {"title":"Masses of the two objects","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"poly\",\"coords\":\"113,132\"},{\"shape\":\"rect\",\"coords\":\"263,4,289,30\"},{\"shape\":\"rect\",\"coords\":\"231,3,253,33\"}]"} {"title":"Center-to-center distance between the two objects","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"235,52,255,73\"}]"} {"title":"The gravitational forces are attractive: vector F sub 1 on 2 pulls object 2 toward object 1 and vector F sub 2 on 1 pulls object 1 toward object 2.","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"32,40,56,59\"},{\"shape\":\"rect\",\"coords\":\"134,42,156,61\"}]"}

Question

LMP4MOB8r+d1yzLOdKTbwj8EPGomhMh072hoe+Pt4/SBRA8v+KTdcrL4JifJtIPqbbJ+CaI4CXo=
{"title":"Any two objects exert equally strong gravitational forces on each \perpher.","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"1,23,28,63\"},{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"102,19,133,60\"}]"} {"title":"Gravitational constant (same for any two objects)","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"201,1,230,32\"}]"} {"title":"Masses of the two objects","description":"Wrong","type":"incorrect","color":"#333300","code":"[{\"shape\":\"poly\",\"coords\":\"113,132\"},{\"shape\":\"rect\",\"coords\":\"263,4,289,30\"},{\"shape\":\"rect\",\"coords\":\"231,3,253,33\"}]"} {"title":"Center-to-center distance between the two objects","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"235,52,255,73\"}]"} {"title":"The gravitational forces are attractive: vector F sub 1 on 2 pulls object 2 toward object 1 and vector F sub 2 on 1 pulls object 1 toward object 2.","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"32,40,56,59\"},{\"shape\":\"rect\",\"coords\":\"134,42,156,61\"}]"}

Question

TB/vmZ341Ct3P6R+gFwpI5NKfAC2GXJT8herP04b/4KJLTK/MF//yTbNcgN5IOcQBC5ae2nse/lbK19/7VFoBIxHr8rxmTj8MqzhW9pSvejeCHRcw+HT0l2FJ2gW3bZ8EE8CHQuIedBogc2EMi4AbjGbkeWTJwMWh1+bynfcLRPgUDVuj/FMSHMIw2rty2bayfzgZteVNs5Uyy7TN7OwXbP/Ibk=
{"title":"Any two objects exert equally strong gravitational forces on each \perpher.","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"1,23,28,63\"},{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"102,19,133,60\"}]"} {"title":"Gravitational constant (same for any two objects)","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"201,1,230,32\"}]"} {"title":"Masses of the two objects","description":"Wrong","type":"incorrect","color":"#333300","code":"[{\"shape\":\"poly\",\"coords\":\"113,132\"},{\"shape\":\"rect\",\"coords\":\"263,4,289,30\"},{\"shape\":\"rect\",\"coords\":\"231,3,253,33\"}]"} {"title":"Center-to-center distance between the two objects","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"235,52,255,73\"}]"} {"title":"The gravitational forces are attractive: vector F sub 1 on 2 pulls object 2 toward object 1 and vector F sub 2 on 1 pulls object 1 toward object 2.","description":"Correct!","type":"correct","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"32,40,56,59\"},{\"shape\":\"rect\",\"coords\":\"134,42,156,61\"}]"}

Review

For the force of Earth on the Moon, \(m_2\) is the Moon’s mass and \(r\) is the Earth-Moon distance. If Equation 10-1 is true for any two objects, then it must also be true that the object of mass \(m_2\) exerts a gravitational force on the object of mass \(m_1\), and this force is directly proportional to the mass \(m_1\). But Newton’s third law (Section 4-5) tells us that the forces that the two objects exert on each \perpher have opposite directions and the same magnitude: \(F_{\mathrm{2\ on\ 1}} = F_{\mathrm{1\ on\ 2}}\). Hence the gravitational force that each object exerts on the \perpher must be directly proportional to both \(m_1\) and \(m_2\). This chain of reasoning leads us to Newton’s law of universal gravitation: